Yamada-Watanabe Theorem for Stochastic Evolution Equation Driven by Poisson Random Measure

Yamada-watanabe Theorem for Stochastic Evolution Equations in Infinite Dimensions

The purpose of this note is to give a complete and detailed proof of the fundamental Yamada-Watanabe Theorem on infinite dimensional spaces, more precisely in the framework of the variational approach to stochastic partial differential equations. 1. Framework and Definitions Let H be a separable Hilbert space, with inner product 〈·, ·〉H and norm ‖·‖H . Let V,E be separable Banach spaces with no...

Multidimensional Yamada-watanabe Theorem and Its Applications

Multidimensional and matrix versions of the Yamada-Watanabe theorem are proved. They are applied to particle systems of squared Bessel processes and to matrix analogues of squared Bessel processes: Wishart and Jacobi matrix processes.

The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities

A general version of the Yamada-Watanabe and Engelbert results relating existence and uniqueness of strong and weak solutions for stochastic equations is given. The results apply to a wide variety of stochastic equations including classical stochastic differential equations, stochastic partial differential equations, and equations involving multiple time transformations.

Multidimensional Yamada-Watanabe theorem and its applications to particle systems

The Yamada-Watanabe theorem for mild solutions to stochastic partial differential equations

We prove the Yamada-Watanabe Theorem for semilinear stochastic partial differential equations with path-dependent coefficients. The so-called “method of the moving frame” allows us to reduce the proof to the Yamada-Watanabe Theorem for stochastic differential equations in infinite dimensions.